In many prior art borehole survey systems, a probe is used that includes acceleration or inclinometer measuring instruments in combination with azimuth or direction determining instruments such as magnetometers. Examples of such systems are provided in U.S. Pat. Nos. 3,862,499 and 4,362,054 which disclose borehole surveying instruments using an inclinometer that includes three accelerometers to measure deviation of the borehole from vertical along with a three axis magnetometer for azimuth determination. Such systems are subject to errors due to a number of factors including variations in the earth's magnetic field caused by the nature of the material through which the borehole passes. There have also been a number of systems that have used gimballed or strapdown mechanical gyros in place of the magnetometers for direction or rotation sensing. However, due to sensitivity to shock and vibration, mechanical gyroscopes do not provide the desired accuracy and reliability for borehole systems. Further, mechanical gyros are subject to drift and precession errors and require substantial settling periods for stabilization. These instruments also tend to be mechanically complex, as well as expensive.
One approach for reducing the errors inherent in making inertial-type measurements of the probe location in a borehole has been the use of Kalman filtering. However, up to the present time, the use of Kalman filtering has been limited to alignment of the probe when stopped in the borehole and has not been used in a dynamic sense for error reduction in measurements made while the probe is moving within the borehole.